What is a Permutations and Combinations Calculator?

The Permutations and Combinations Calculator (sometimes called an nPr and nCr calculator) computes how many possible arrangements and selections can be made from a given set of items. Permutations count outcomes where order matters. Combinations count outcomes where order does not matter. This calculator is commonly used in probability, statistics, sports betting models, and real-world planning scenarios — such as tournament brackets, lottery odds, or lineup combinations.

How do you calculate permutations and combinations?

The calculator uses standard mathematical formulas to determine the number of possible outcomes. Permutations — when order matters: P(n, k) = n! / (n − k)!, where n is the total number of items, k is the number of items selected, and ! (factorial) is the product of all positive integers up to n. Combinations — when order doesn’t matter: C(n, k) = n! / (k! × (n − k)!), where the factorial values calculate all unique groupings regardless of order. Factorial (n!): n! = n × (n − 1) × (n − 2) × ... × 1. Factorials grow quickly and are the backbone of both permutation and combination calculations.

How does this calculator help me?

The Permutations & Combinations Calculator simplifies complex math instantly, helping users evaluate probabilities, plan outcomes, and analyze data. It is especially useful for sports bettors modeling parlay probabilities or event outcomes, students studying combinatorics or probability theory, and analysts and planners calculating unique possibilities or distributions. Whether you are comparing potential lineup outcomes or exploring statistical probabilities, this tool provides fast, accurate, and educational results tailored for both academic and practical use.

Bettor Ed Permutations & Combinations Calculator

Enter n and k to get the number of permutations and combinations

Frequently Asked Questions

Find answers to commonly asked questions about the Permutations and Combinations Calculator

What is a Permutations and Combinations Calculator?
- The Permutations and Combinations Calculator (sometimes called an nPr and nCr calculator) computes how many possible arrangements and selections can be made from a given set of items.
  - Permutations count outcomes where order matters.
  - Combinations count outcomes where order does not matter.
  - This calculator is commonly used in probability, statistics, sports betting models, and real-world planning scenarios — such as tournament brackets, lottery odds, or lineup combinations.

How do you calculate permutations and combinations?
- The calculator uses standard mathematical formulas to determine the number of possible outcomes:
  - Permutations — when order matters
    - Formula:
      P(n, k) = n! / (n − k)!
      Where:
    - n = total number of items
    - k = number of items selected
    - ! = factorial, the product of all positive integers up to n
  - Combinations — when order doesn’t matter
    - Formula:
      C(n, k) = n! / (k! × (n − k)!)
      Where the factorial values calculate all unique groupings regardless of order.
    - Factorial (n!)
    - Definition:
      n! = n × (n − 1) × (n − 2) × ... × 1
  - Factorials grow quickly and are the backbone of both permutation and combination calculations.

How does this calculator help me?
- The Permutations & Combinations Calculator simplifies complex math instantly, helping users evaluate probabilities, plan outcomes, and analyze data.
- It’s especially useful for:
  - Sports bettors modeling parlay probabilities or event outcomes.
  - Students studying combinatorics or probability theory.
  - Analysts and planners calculating unique possibilities or distributions.
  - Whether you’re comparing potential lineup outcomes or exploring statistical probabilities, this tool provides fast, accurate, and educational results tailored for both academic and practical use.